Some combinatorial matrices and their LU-decomposition

TL;DR

This paper investigates three specific combinatorial matrices, deriving their LU-decompositions through a combination of insightful guessing and straightforward proof techniques.

Contribution

It provides explicit LU-decompositions for three combinatorial matrices, a task often approached by guesswork and routine calculations.

Findings

Explicit LU-decompositions derived

Methodology combines creative guessing with routine proofs

Enhances understanding of combinatorial matrix structures

Abstract

Three combinatorial matrices are considered and their LU-decompositions were found. This is typically done by (creative) guessing, and necessary proofs are more or less routine calculations.